Redo some figures for the huddle test
Before Width: | Height: | Size: 95 KiB After Width: | Height: | Size: 115 KiB |
Before Width: | Height: | Size: 46 KiB After Width: | Height: | Size: 54 KiB |
Before Width: | Height: | Size: 130 KiB After Width: | Height: | Size: 177 KiB |
Before Width: | Height: | Size: 116 KiB After Width: | Height: | Size: 157 KiB |
Before Width: | Height: | Size: 96 KiB After Width: | Height: | Size: 139 KiB |
Before Width: | Height: | Size: 83 KiB After Width: | Height: | Size: 100 KiB |
@ -3,7 +3,7 @@
|
|||||||
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-strict.dtd">
|
||||||
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
<html xmlns="http://www.w3.org/1999/xhtml" lang="en" xml:lang="en">
|
||||||
<head>
|
<head>
|
||||||
<!-- 2019-05-02 jeu. 14:11 -->
|
<!-- 2019-05-03 ven. 08:40 -->
|
||||||
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
<meta http-equiv="Content-Type" content="text/html;charset=utf-8" />
|
||||||
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
<meta name="viewport" content="width=device-width, initial-scale=1" />
|
||||||
<title>Huddle Test of the L22 Geophones</title>
|
<title>Huddle Test of the L22 Geophones</title>
|
||||||
@ -276,36 +276,36 @@ for the JavaScript code in this tag.
|
|||||||
<h2>Table of Contents</h2>
|
<h2>Table of Contents</h2>
|
||||||
<div id="text-table-of-contents">
|
<div id="text-table-of-contents">
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orge5c8cc5">1. Experimental Setup</a></li>
|
<li><a href="#org6392291">1. Experimental Setup</a></li>
|
||||||
<li><a href="#org8b7c96e">2. Signal Processing</a>
|
<li><a href="#orgb55c46d">2. Signal Processing</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org7cb3283">2.1. Load data</a></li>
|
<li><a href="#org016f692">2.1. Load data</a></li>
|
||||||
<li><a href="#org0a3a0d0">2.2. Time Domain Data</a></li>
|
<li><a href="#orgc616389">2.2. Time Domain Data</a></li>
|
||||||
<li><a href="#org89016b8">2.3. Computation of the ASD of the measured voltage</a></li>
|
<li><a href="#org8794282">2.3. Computation of the ASD of the measured voltage</a></li>
|
||||||
<li><a href="#orga26e03c">2.4. Scaling to take into account the sensibility of the geophone and the voltage amplifier</a></li>
|
<li><a href="#org09670e4">2.4. Scaling to take into account the sensibility of the geophone and the voltage amplifier</a></li>
|
||||||
<li><a href="#orgfd3ab32">2.5. Computation of the ASD of the velocity</a></li>
|
<li><a href="#org4e5224a">2.5. Computation of the ASD of the velocity</a></li>
|
||||||
<li><a href="#orgcd33ee8">2.6. Transfer function between the two geophones</a></li>
|
<li><a href="#orge366f60">2.6. Transfer function between the two geophones</a></li>
|
||||||
<li><a href="#org244b412">2.7. Estimation of the sensor noise</a></li>
|
<li><a href="#org4cacf62">2.7. Estimation of the sensor noise</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org6beee86">3. Compare axis</a>
|
<li><a href="#org559b5b9">3. Compare axis</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#org53cf537">3.1. Load data</a></li>
|
<li><a href="#org24b196e">3.1. Load data</a></li>
|
||||||
<li><a href="#org8e12607">3.2. Compare PSD</a></li>
|
<li><a href="#org00c635c">3.2. Compare PSD</a></li>
|
||||||
<li><a href="#org90e5861">3.3. Compare TF</a></li>
|
<li><a href="#org16927e1">3.3. Compare TF</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
<li><a href="#org7c0ad67">4. Appendix</a>
|
<li><a href="#orgf4800f0">4. Appendix</a>
|
||||||
<ul>
|
<ul>
|
||||||
<li><a href="#orgd75efe3">4.1. Computation of coherence from PSD and CSD</a></li>
|
<li><a href="#org556257c">4.1. Computation of coherence from PSD and CSD</a></li>
|
||||||
</ul>
|
</ul>
|
||||||
</li>
|
</li>
|
||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orge5c8cc5" class="outline-2">
|
<div id="outline-container-org6392291" class="outline-2">
|
||||||
<h2 id="orge5c8cc5"><span class="section-number-2">1</span> Experimental Setup</h2>
|
<h2 id="org6392291"><span class="section-number-2">1</span> Experimental Setup</h2>
|
||||||
<div class="outline-text-2" id="text-1">
|
<div class="outline-text-2" id="text-1">
|
||||||
<p>
|
<p>
|
||||||
Two L22 geophones are used.
|
Two L22 geophones are used.
|
||||||
@ -319,14 +319,14 @@ The voltage amplifiers include a low pass filter with a cut-off frequency at 1kH
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="org32e95c2" class="figure">
|
<div id="orgddb9341" class="figure">
|
||||||
<p><img src="./figs/setup.jpg" alt="setup.jpg" width="500px" />
|
<p><img src="./figs/setup.jpg" alt="setup.jpg" width="500px" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 1: </span>Setup</p>
|
<p><span class="figure-number">Figure 1: </span>Setup</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="orgdd8ca8c" class="figure">
|
<div id="org8077b6d" class="figure">
|
||||||
<p><img src="./figs/geophones.jpg" alt="geophones.jpg" width="500px" />
|
<p><img src="./figs/geophones.jpg" alt="geophones.jpg" width="500px" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 2: </span>Geophones</p>
|
<p><span class="figure-number">Figure 2: </span>Geophones</p>
|
||||||
@ -334,8 +334,8 @@ The voltage amplifiers include a low pass filter with a cut-off frequency at 1kH
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org8b7c96e" class="outline-2">
|
<div id="outline-container-orgb55c46d" class="outline-2">
|
||||||
<h2 id="org8b7c96e"><span class="section-number-2">2</span> Signal Processing</h2>
|
<h2 id="orgb55c46d"><span class="section-number-2">2</span> Signal Processing</h2>
|
||||||
<div class="outline-text-2" id="text-2">
|
<div class="outline-text-2" id="text-2">
|
||||||
<p>
|
<p>
|
||||||
The Matlab computing file for this part is accessible <a href="signal_processing.m">here</a>.
|
The Matlab computing file for this part is accessible <a href="signal_processing.m">here</a>.
|
||||||
@ -343,8 +343,8 @@ The <code>mat</code> file containing the measurement data is accessible <a href=
|
|||||||
</p>
|
</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org7cb3283" class="outline-3">
|
<div id="outline-container-org016f692" class="outline-3">
|
||||||
<h3 id="org7cb3283"><span class="section-number-3">2.1</span> Load data</h3>
|
<h3 id="org016f692"><span class="section-number-3">2.1</span> Load data</h3>
|
||||||
<div class="outline-text-3" id="text-2-1">
|
<div class="outline-text-3" id="text-2-1">
|
||||||
<p>
|
<p>
|
||||||
We load the data of the z axis of two geophones.
|
We load the data of the z axis of two geophones.
|
||||||
@ -358,8 +358,8 @@ dt = t<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-high
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org0a3a0d0" class="outline-3">
|
<div id="outline-container-orgc616389" class="outline-3">
|
||||||
<h3 id="org0a3a0d0"><span class="section-number-3">2.2</span> Time Domain Data</h3>
|
<h3 id="orgc616389"><span class="section-number-3">2.2</span> Time Domain Data</h3>
|
||||||
<div class="outline-text-3" id="text-2-2">
|
<div class="outline-text-3" id="text-2-2">
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||||
@ -374,7 +374,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org09ad879" class="figure">
|
<div id="orgeb104f7" class="figure">
|
||||||
<p><img src="figs/data_time_domain.png" alt="data_time_domain.png" />
|
<p><img src="figs/data_time_domain.png" alt="data_time_domain.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 3: </span>Time domain Data</p>
|
<p><span class="figure-number">Figure 3: </span>Time domain Data</p>
|
||||||
@ -394,7 +394,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org04c8d74" class="figure">
|
<div id="orgd0dc39d" class="figure">
|
||||||
<p><img src="figs/data_time_domain_zoom.png" alt="data_time_domain_zoom.png" />
|
<p><img src="figs/data_time_domain_zoom.png" alt="data_time_domain_zoom.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 4: </span>Time domain Data - Zoom</p>
|
<p><span class="figure-number">Figure 4: </span>Time domain Data - Zoom</p>
|
||||||
@ -402,15 +402,15 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org89016b8" class="outline-3">
|
<div id="outline-container-org8794282" class="outline-3">
|
||||||
<h3 id="org89016b8"><span class="section-number-3">2.3</span> Computation of the ASD of the measured voltage</h3>
|
<h3 id="org8794282"><span class="section-number-3">2.3</span> Computation of the ASD of the measured voltage</h3>
|
||||||
<div class="outline-text-3" id="text-2-3">
|
<div class="outline-text-3" id="text-2-3">
|
||||||
<p>
|
<p>
|
||||||
We first define the parameters for the frequency domain analysis.
|
We first define the parameters for the frequency domain analysis.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span>length<span class="org-rainbow-delimiters-depth-3">(</span>x1<span class="org-rainbow-delimiters-depth-3">)</span><span class="org-type">/</span><span class="org-highlight-numbers-number">100</span><span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
<pre class="src src-matlab">Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt;
|
||||||
Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/</span>dt;
|
win = hanning<span class="org-rainbow-delimiters-depth-1">(</span>ceil<span class="org-rainbow-delimiters-depth-2">(</span><span class="org-highlight-numbers-number">10</span><span class="org-type">*</span>Fs<span class="org-rainbow-delimiters-depth-2">)</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
@ -422,12 +422,12 @@ Fs = <span class="org-highlight-numbers-number">1</span><span class="org-type">/
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orga26e03c" class="outline-3">
|
<div id="outline-container-org09670e4" class="outline-3">
|
||||||
<h3 id="orga26e03c"><span class="section-number-3">2.4</span> Scaling to take into account the sensibility of the geophone and the voltage amplifier</h3>
|
<h3 id="org09670e4"><span class="section-number-3">2.4</span> Scaling to take into account the sensibility of the geophone and the voltage amplifier</h3>
|
||||||
<div class="outline-text-3" id="text-2-4">
|
<div class="outline-text-3" id="text-2-4">
|
||||||
<p>
|
<p>
|
||||||
The Geophone used are L22.
|
The Geophone used are L22.
|
||||||
Their sensibility are shown on figure <a href="#orgb86dfe6">5</a>.
|
Their sensibility are shown on figure <a href="#orgdbecac7">5</a>.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
@ -438,7 +438,7 @@ S = <span class="org-rainbow-delimiters-depth-1">(</span>s<span class="org-type"
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="orgb86dfe6" class="figure">
|
<div id="orgdbecac7" class="figure">
|
||||||
<p><img src="figs/geophone_sensibility.png" alt="geophone_sensibility.png" />
|
<p><img src="figs/geophone_sensibility.png" alt="geophone_sensibility.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 5: </span>Sensibility of the Geophone</p>
|
<p><span class="figure-number">Figure 5: </span>Sensibility of the Geophone</p>
|
||||||
@ -469,11 +469,11 @@ We further divide the result by the sensibility of the Geophone to obtain the AS
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgfd3ab32" class="outline-3">
|
<div id="outline-container-org4e5224a" class="outline-3">
|
||||||
<h3 id="orgfd3ab32"><span class="section-number-3">2.5</span> Computation of the ASD of the velocity</h3>
|
<h3 id="org4e5224a"><span class="section-number-3">2.5</span> Computation of the ASD of the velocity</h3>
|
||||||
<div class="outline-text-3" id="text-2-5">
|
<div class="outline-text-3" id="text-2-5">
|
||||||
<p>
|
<p>
|
||||||
The ASD of the measured velocity is shown on figure <a href="#org204dcef">6</a>.
|
The ASD of the measured velocity is shown on figure <a href="#orgf6e310e">6</a>.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
@ -485,19 +485,19 @@ hold off;
|
|||||||
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'PSD </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s/sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">(</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'PSD </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s/sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">(</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
||||||
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org204dcef" class="figure">
|
<div id="orgf6e310e" class="figure">
|
||||||
<p><img src="figs/psd_velocity.png" alt="psd_velocity.png" />
|
<p><img src="figs/psd_velocity.png" alt="psd_velocity.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 6: </span>Spectral density of the velocity</p>
|
<p><span class="figure-number">Figure 6: </span>Spectral density of the velocity</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
We also plot the ASD in displacement (figure <a href="#org9967b3b">7</a>);
|
We also plot the ASD in displacement (figure <a href="#org0ea2712">7</a>);
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
@ -508,12 +508,12 @@ plot<span class="org-rainbow-delimiters-depth-1">(</span>f, <span class="org-rai
|
|||||||
hold off;
|
hold off;
|
||||||
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'PSD </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s/sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">(</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'PSD </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">m/s/sqrt</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">(</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-3">)</span></span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-rainbow-delimiters-depth-1">)</span>
|
||||||
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">2</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org9967b3b" class="figure">
|
<div id="org0ea2712" class="figure">
|
||||||
<p><img src="figs/asd_displacement.png" alt="asd_displacement.png" />
|
<p><img src="figs/asd_displacement.png" alt="asd_displacement.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the displacement as measured by the geophones</p>
|
<p><span class="figure-number">Figure 7: </span>Amplitude Spectral Density of the displacement as measured by the geophones</p>
|
||||||
@ -521,16 +521,16 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-orgcd33ee8" class="outline-3">
|
<div id="outline-container-orge366f60" class="outline-3">
|
||||||
<h3 id="orgcd33ee8"><span class="section-number-3">2.6</span> Transfer function between the two geophones</h3>
|
<h3 id="orge366f60"><span class="section-number-3">2.6</span> Transfer function between the two geophones</h3>
|
||||||
<div class="outline-text-3" id="text-2-6">
|
<div class="outline-text-3" id="text-2-6">
|
||||||
<p>
|
<p>
|
||||||
We here compute the transfer function from one geophone to the other.
|
We here compute the transfer function from one geophone to the other.
|
||||||
The result is shown on figure <a href="#org5faacba">8</a>.
|
The result is shown on figure <a href="#orgba6f718">8</a>.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
We also compute the coherence between the two signals (figure <a href="#orgf374e25">9</a>).
|
We also compute the coherence between the two signals (figure <a href="#org251a7af">9</a>).
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
@ -539,7 +539,7 @@ We also compute the coherence between the two signals (figure <a href="#orgf374e
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org5faacba" class="figure">
|
<div id="orgba6f718" class="figure">
|
||||||
<p><img src="figs/tf_geophones.png" alt="tf_geophones.png" />
|
<p><img src="figs/tf_geophones.png" alt="tf_geophones.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 8: </span>Estimated transfer function between the two geophones</p>
|
<p><span class="figure-number">Figure 8: </span>Estimated transfer function between the two geophones</p>
|
||||||
@ -551,7 +551,7 @@ We also compute the coherence between the two signals (figure <a href="#orgf374e
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="orgf374e25" class="figure">
|
<div id="org251a7af" class="figure">
|
||||||
<p><img src="figs/coh_geophones.png" alt="coh_geophones.png" />
|
<p><img src="figs/coh_geophones.png" alt="coh_geophones.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 9: </span>Cohererence between the signals of the two geophones</p>
|
<p><span class="figure-number">Figure 9: </span>Cohererence between the signals of the two geophones</p>
|
||||||
@ -559,8 +559,8 @@ We also compute the coherence between the two signals (figure <a href="#orgf374e
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org244b412" class="outline-3">
|
<div id="outline-container-org4cacf62" class="outline-3">
|
||||||
<h3 id="org244b412"><span class="section-number-3">2.7</span> Estimation of the sensor noise</h3>
|
<h3 id="org4cacf62"><span class="section-number-3">2.7</span> Estimation of the sensor noise</h3>
|
||||||
<div class="outline-text-3" id="text-2-7">
|
<div class="outline-text-3" id="text-2-7">
|
||||||
<p>
|
<p>
|
||||||
The technique to estimate the sensor noise is taken from <a class='org-ref-reference' href="#barzilai98_techn_measur_noise_sensor_presen">barzilai98_techn_measur_noise_sensor_presen</a>.
|
The technique to estimate the sensor noise is taken from <a class='org-ref-reference' href="#barzilai98_techn_measur_noise_sensor_presen">barzilai98_techn_measur_noise_sensor_presen</a>.
|
||||||
@ -590,11 +590,11 @@ where:
|
|||||||
</ul>
|
</ul>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
The <code>mscohere</code> function is compared with this formula on Appendix (section <a href="#orge316ad4">4.1</a>), it is shown that it is identical.
|
The <code>mscohere</code> function is compared with this formula on Appendix (section <a href="#org1e77eec">4.1</a>), it is shown that it is identical.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
Figure <a href="#org57a5459">10</a> illustrate a block diagram model of the system used to determine the sensor noise of the geophone.
|
Figure <a href="#org8c23b33">10</a> illustrate a block diagram model of the system used to determine the sensor noise of the geophone.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
@ -606,7 +606,7 @@ Each sensor has noise \(N\) and \(M\).
|
|||||||
</p>
|
</p>
|
||||||
|
|
||||||
|
|
||||||
<div id="org57a5459" class="figure">
|
<div id="org8c23b33" class="figure">
|
||||||
<p><img src="figs/huddle-test.png" alt="huddle-test.png" />
|
<p><img src="figs/huddle-test.png" alt="huddle-test.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 10: </span>Huddle test block diagram</p>
|
<p><span class="figure-number">Figure 10: </span>Huddle test block diagram</p>
|
||||||
@ -621,7 +621,7 @@ We also assume that \(S_1 = S_2 = 1\).
|
|||||||
We then obtain:
|
We then obtain:
|
||||||
</p>
|
</p>
|
||||||
\begin{equation}
|
\begin{equation}
|
||||||
\label{org5b2976f}
|
\label{org3a8a59f}
|
||||||
\gamma_{XY}^2(\omega) = \frac{1}{1 + 2 \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right) + \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right)^2}
|
\gamma_{XY}^2(\omega) = \frac{1}{1 + 2 \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right) + \left( \frac{|G_N(\omega)|}{|G_U(\omega)|} \right)^2}
|
||||||
\end{equation}
|
\end{equation}
|
||||||
|
|
||||||
@ -629,23 +629,23 @@ We then obtain:
|
|||||||
Since the input signal \(U\) and the instrumental noise \(N\) are incoherent:
|
Since the input signal \(U\) and the instrumental noise \(N\) are incoherent:
|
||||||
</p>
|
</p>
|
||||||
\begin{equation}
|
\begin{equation}
|
||||||
\label{orgb493a2c}
|
\label{org221f31e}
|
||||||
|G_X(\omega)| = |G_N(\omega)| + |G_U(\omega)|
|
|G_X(\omega)| = |G_N(\omega)| + |G_U(\omega)|
|
||||||
\end{equation}
|
\end{equation}
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
From equations \eqref{org5b2976f} and \eqref{orgb493a2c}, we finally obtain
|
From equations \eqref{org3a8a59f} and \eqref{org221f31e}, we finally obtain
|
||||||
</p>
|
</p>
|
||||||
<div class="important">
|
<div class="important">
|
||||||
\begin{equation}
|
\begin{equation}
|
||||||
\label{org4f59d30}
|
\label{org3574759}
|
||||||
|G_N(\omega)| = |G_X(\omega)| \left( 1 - \sqrt{\gamma_{XY}^2(\omega)} \right)
|
|G_N(\omega)| = |G_X(\omega)| \left( 1 - \sqrt{\gamma_{XY}^2(\omega)} \right)
|
||||||
\end{equation}
|
\end{equation}
|
||||||
|
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
The instrumental noise is computed below. The result in V<sup>2</sup>/Hz is shown on figure <a href="#org9584668">11</a>.
|
The instrumental noise is computed below. The result in V<sup>2</sup>/Hz is shown on figure <a href="#orge1676ed">11</a>.
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">pxxN = pxx1<span class="org-type">.*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span> <span class="org-type">-</span> coh12<span class="org-rainbow-delimiters-depth-1">)</span>;
|
<pre class="src src-matlab">pxxN = pxx1<span class="org-type">.*</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-highlight-numbers-number">1</span> <span class="org-type">-</span> coh12<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
@ -661,19 +661,19 @@ plot<span class="org-rainbow-delimiters-depth-1">(</span>f, pxxN, <span class="o
|
|||||||
hold off;
|
hold off;
|
||||||
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
xlabel<span class="org-rainbow-delimiters-depth-1">(</span>'Frequency <span class="org-rainbow-delimiters-depth-2">[</span>Hz<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span>'PSD <span class="org-rainbow-delimiters-depth-2">[</span>$V<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span>Hz$<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span>'Frequency <span class="org-rainbow-delimiters-depth-2">[</span>Hz<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>; ylabel<span class="org-rainbow-delimiters-depth-1">(</span>'PSD <span class="org-rainbow-delimiters-depth-2">[</span>$V<span class="org-type">^</span><span class="org-highlight-numbers-number">2</span><span class="org-type">/</span>Hz$<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org9584668" class="figure">
|
<div id="orge1676ed" class="figure">
|
||||||
<p><img src="figs/intrumental_noise_V.png" alt="intrumental_noise_V.png" />
|
<p><img src="figs/intrumental_noise_V.png" alt="intrumental_noise_V.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 11: </span>Instrumental Noise and Measurement in \(V^2/Hz\)</p>
|
<p><span class="figure-number">Figure 11: </span>Instrumental Noise and Measurement in \(V^2/Hz\)</p>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
This is then further converted into velocity and compared with the ground velocity measurement. (figure <a href="#orgdd66b8f">12</a>)
|
This is then further converted into velocity and compared with the ground velocity measurement. (figure <a href="#org30e84b0">12</a>)
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
<pre class="src src-matlab"><span class="org-type">figure</span>;
|
||||||
@ -684,12 +684,12 @@ plot<span class="org-rainbow-delimiters-depth-1">(</span>f, sqrt<span class="org
|
|||||||
hold off;
|
hold off;
|
||||||
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
<span class="org-type">set</span><span class="org-rainbow-delimiters-depth-1">(</span><span class="org-variable-name">gca</span>, <span class="org-string">'xscale', 'log'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; set</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">gca, 'yscale', 'log'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>PSD <span class="org-rainbow-delimiters-depth-2">[</span>$m<span class="org-type">/</span>s<span class="org-type">/\</span>sqrt<span class="org-rainbow-delimiters-depth-3">{</span>Hz<span class="org-rainbow-delimiters-depth-3">}</span>$<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
xlabel<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'Frequency </span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">[</span></span><span class="org-string">Hz</span><span class="org-string"><span class="org-rainbow-delimiters-depth-2">]</span></span><span class="org-string">'</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">)</span></span><span class="org-string">; ylabel</span><span class="org-string"><span class="org-rainbow-delimiters-depth-1">(</span></span><span class="org-string">'</span>PSD <span class="org-rainbow-delimiters-depth-2">[</span>$m<span class="org-type">/</span>s<span class="org-type">/\</span>sqrt<span class="org-rainbow-delimiters-depth-3">{</span>Hz<span class="org-rainbow-delimiters-depth-3">}</span>$<span class="org-rainbow-delimiters-depth-2">]</span>'<span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbow-delimiters-depth-2">[</span><span class="org-highlight-numbers-number">0</span>.<span class="org-highlight-numbers-number">1</span>, <span class="org-highlight-numbers-number">500</span><span class="org-rainbow-delimiters-depth-2">]</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
</pre>
|
</pre>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="orgdd66b8f" class="figure">
|
<div id="org30e84b0" class="figure">
|
||||||
<p><img src="figs/intrumental_noise_velocity.png" alt="intrumental_noise_velocity.png" />
|
<p><img src="figs/intrumental_noise_velocity.png" alt="intrumental_noise_velocity.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 12: </span>Instrumental Noise and Measurement in \(m/s/\sqrt{Hz}\)</p>
|
<p><span class="figure-number">Figure 12: </span>Instrumental Noise and Measurement in \(m/s/\sqrt{Hz}\)</p>
|
||||||
@ -698,8 +698,8 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org6beee86" class="outline-2">
|
<div id="outline-container-org559b5b9" class="outline-2">
|
||||||
<h2 id="org6beee86"><span class="section-number-2">3</span> Compare axis</h2>
|
<h2 id="org559b5b9"><span class="section-number-2">3</span> Compare axis</h2>
|
||||||
<div class="outline-text-2" id="text-3">
|
<div class="outline-text-2" id="text-3">
|
||||||
<p>
|
<p>
|
||||||
The Matlab computing file for this part is accessible <a href="compare_axis.m">here</a>.
|
The Matlab computing file for this part is accessible <a href="compare_axis.m">here</a>.
|
||||||
@ -712,8 +712,8 @@ The <code>mat</code> files containing the measurement data are accessible with t
|
|||||||
</ul>
|
</ul>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org53cf537" class="outline-3">
|
<div id="outline-container-org24b196e" class="outline-3">
|
||||||
<h3 id="org53cf537"><span class="section-number-3">3.1</span> Load data</h3>
|
<h3 id="org24b196e"><span class="section-number-3">3.1</span> Load data</h3>
|
||||||
<div class="outline-text-3" id="text-3-1">
|
<div class="outline-text-3" id="text-3-1">
|
||||||
<p>
|
<p>
|
||||||
We first load the data for the three axis.
|
We first load the data for the three axis.
|
||||||
@ -727,8 +727,8 @@ north = load<span class="org-rainbow-delimiters-depth-1">(</span><span class="or
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org8e12607" class="outline-3">
|
<div id="outline-container-org00c635c" class="outline-3">
|
||||||
<h3 id="org8e12607"><span class="section-number-3">3.2</span> Compare PSD</h3>
|
<h3 id="org00c635c"><span class="section-number-3">3.2</span> Compare PSD</h3>
|
||||||
<div class="outline-text-3" id="text-3-2">
|
<div class="outline-text-3" id="text-3-2">
|
||||||
<p>
|
<p>
|
||||||
The PSD for each axis of the two geophones are computed.
|
The PSD for each axis of the two geophones are computed.
|
||||||
@ -746,10 +746,10 @@ The PSD for each axis of the two geophones are computed.
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
<p>
|
<p>
|
||||||
We compare them. The result is shown on figure <a href="#org4b31119">13</a>.
|
We compare them. The result is shown on figure <a href="#org6734ed2">13</a>.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div id="org4b31119" class="figure">
|
<div id="org6734ed2" class="figure">
|
||||||
<p><img src="figs/compare_axis_psd.png" alt="compare_axis_psd.png" />
|
<p><img src="figs/compare_axis_psd.png" alt="compare_axis_psd.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 13: </span>Compare the measure PSD of the two geophones for the three axis</p>
|
<p><span class="figure-number">Figure 13: </span>Compare the measure PSD of the two geophones for the three axis</p>
|
||||||
@ -757,12 +757,12 @@ We compare them. The result is shown on figure <a href="#org4b31119">13</a>.
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org90e5861" class="outline-3">
|
<div id="outline-container-org16927e1" class="outline-3">
|
||||||
<h3 id="org90e5861"><span class="section-number-3">3.3</span> Compare TF</h3>
|
<h3 id="org16927e1"><span class="section-number-3">3.3</span> Compare TF</h3>
|
||||||
<div class="outline-text-3" id="text-3-3">
|
<div class="outline-text-3" id="text-3-3">
|
||||||
<p>
|
<p>
|
||||||
The transfer functions from one geophone to the other are also computed for each axis.
|
The transfer functions from one geophone to the other are also computed for each axis.
|
||||||
The result is shown on figure <a href="#org76b2565">14</a>.
|
The result is shown on figure <a href="#org8df4d36">14</a>.
|
||||||
</p>
|
</p>
|
||||||
|
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
@ -773,7 +773,7 @@ The result is shown on figure <a href="#org76b2565">14</a>.
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org76b2565" class="figure">
|
<div id="org8df4d36" class="figure">
|
||||||
<p><img src="figs/compare_tf_axis.png" alt="compare_tf_axis.png" />
|
<p><img src="figs/compare_tf_axis.png" alt="compare_tf_axis.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 14: </span>Compare the transfer function from one geophone to the other for the 3 axis</p>
|
<p><span class="figure-number">Figure 14: </span>Compare the transfer function from one geophone to the other for the 3 axis</p>
|
||||||
@ -782,15 +782,15 @@ The result is shown on figure <a href="#org76b2565">14</a>.
|
|||||||
</div>
|
</div>
|
||||||
</div>
|
</div>
|
||||||
|
|
||||||
<div id="outline-container-org7c0ad67" class="outline-2">
|
<div id="outline-container-orgf4800f0" class="outline-2">
|
||||||
<h2 id="org7c0ad67"><span class="section-number-2">4</span> Appendix</h2>
|
<h2 id="orgf4800f0"><span class="section-number-2">4</span> Appendix</h2>
|
||||||
<div class="outline-text-2" id="text-4">
|
<div class="outline-text-2" id="text-4">
|
||||||
</div>
|
</div>
|
||||||
<div id="outline-container-orgd75efe3" class="outline-3">
|
<div id="outline-container-org556257c" class="outline-3">
|
||||||
<h3 id="orgd75efe3"><span class="section-number-3">4.1</span> Computation of coherence from PSD and CSD</h3>
|
<h3 id="org556257c"><span class="section-number-3">4.1</span> Computation of coherence from PSD and CSD</h3>
|
||||||
<div class="outline-text-3" id="text-4-1">
|
<div class="outline-text-3" id="text-4-1">
|
||||||
<p>
|
<p>
|
||||||
<a id="orge316ad4"></a>
|
<a id="org1e77eec"></a>
|
||||||
</p>
|
</p>
|
||||||
<div class="org-src-container">
|
<div class="org-src-container">
|
||||||
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_001.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
<pre class="src src-matlab">load<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-string">'mat/data_001.mat', 't', 'x1', 'x2'</span><span class="org-rainbow-delimiters-depth-1">)</span>;
|
||||||
@ -821,7 +821,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
|||||||
</div>
|
</div>
|
||||||
|
|
||||||
|
|
||||||
<div id="org5c602bf" class="figure">
|
<div id="org190093c" class="figure">
|
||||||
<p><img src="figs/comp_coherence_formula.png" alt="comp_coherence_formula.png" />
|
<p><img src="figs/comp_coherence_formula.png" alt="comp_coherence_formula.png" />
|
||||||
</p>
|
</p>
|
||||||
<p><span class="figure-number">Figure 15: </span>Comparison of <code>mscohere</code> and manual computation</p>
|
<p><span class="figure-number">Figure 15: </span>Comparison of <code>mscohere</code> and manual computation</p>
|
||||||
@ -839,7 +839,7 @@ xlim<span class="org-rainbow-delimiters-depth-1">(</span><span class="org-rainbo
|
|||||||
</div>
|
</div>
|
||||||
<div id="postamble" class="status">
|
<div id="postamble" class="status">
|
||||||
<p class="author">Author: Thomas Dehaeze</p>
|
<p class="author">Author: Thomas Dehaeze</p>
|
||||||
<p class="date">Created: 2019-05-02 jeu. 14:11</p>
|
<p class="date">Created: 2019-05-03 ven. 08:40</p>
|
||||||
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
<p class="validation"><a href="http://validator.w3.org/check?uri=referer">Validate</a></p>
|
||||||
</div>
|
</div>
|
||||||
</body>
|
</body>
|
||||||
|
@ -106,8 +106,8 @@ We load the data of the z axis of two geophones.
|
|||||||
** Computation of the ASD of the measured voltage
|
** Computation of the ASD of the measured voltage
|
||||||
We first define the parameters for the frequency domain analysis.
|
We first define the parameters for the frequency domain analysis.
|
||||||
#+begin_src matlab :results none
|
#+begin_src matlab :results none
|
||||||
win = hanning(ceil(length(x1)/100));
|
|
||||||
Fs = 1/dt;
|
Fs = 1/dt;
|
||||||
|
win = hanning(ceil(10*Fs));
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+begin_src matlab :results none
|
#+begin_src matlab :results none
|
||||||
@ -171,12 +171,12 @@ The ASD of the measured velocity is shown on figure [[fig:psd_velocity]].
|
|||||||
set(gca, 'xscale', 'log');
|
set(gca, 'xscale', 'log');
|
||||||
set(gca, 'yscale', 'log');
|
set(gca, 'yscale', 'log');
|
||||||
xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
|
xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
|
||||||
xlim([2, 500]);
|
xlim([0.1, 500]);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+NAME: fig:psd_velocity
|
#+NAME: fig:psd_velocity
|
||||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||||
#+begin_src matlab :var filepath="figs/psd_velocity.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
|
#+begin_src matlab :var filepath="figs/psd_velocity.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
<<plt-matlab>>
|
<<plt-matlab>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
@ -195,12 +195,12 @@ We also plot the ASD in displacement (figure [[fig:asd_displacement]]);
|
|||||||
hold off;
|
hold off;
|
||||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||||
xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
|
xlabel('Frequency [Hz]'); ylabel('PSD [m/s/sqrt(Hz)]')
|
||||||
xlim([2, 500]);
|
xlim([0.1, 500]);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+NAME: fig:asd_displacement
|
#+NAME: fig:asd_displacement
|
||||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||||
#+begin_src matlab :var filepath="figs/asd_displacement.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
|
#+begin_src matlab :var filepath="figs/asd_displacement.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
<<plt-matlab>>
|
<<plt-matlab>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
@ -235,7 +235,7 @@ We also compute the coherence between the two signals (figure [[fig:coh_geophone
|
|||||||
xlabel('Frequency [Hz]'); ylabel('Phase');
|
xlabel('Frequency [Hz]'); ylabel('Phase');
|
||||||
|
|
||||||
linkaxes([ax1,ax2],'x');
|
linkaxes([ax1,ax2],'x');
|
||||||
xlim([1, 500]);
|
xlim([0.1, 500]);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+NAME: fig:tf_geophones
|
#+NAME: fig:tf_geophones
|
||||||
@ -258,7 +258,7 @@ We also compute the coherence between the two signals (figure [[fig:coh_geophone
|
|||||||
plot(f, coh12);
|
plot(f, coh12);
|
||||||
set(gca, 'xscale', 'log');
|
set(gca, 'xscale', 'log');
|
||||||
xlabel('Frequency [Hz]'); ylabel('Coherence');
|
xlabel('Frequency [Hz]'); ylabel('Coherence');
|
||||||
ylim([0,1]); xlim([1, 500]);
|
ylim([0,1]); xlim([0.1, 500]);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+NAME: fig:coh_geophones
|
#+NAME: fig:coh_geophones
|
||||||
@ -339,12 +339,12 @@ The instrumental noise is computed below. The result in V^2/Hz is shown on figur
|
|||||||
hold off;
|
hold off;
|
||||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||||
xlabel('Frequency [Hz]'); ylabel('PSD [$V^2/Hz$]');
|
xlabel('Frequency [Hz]'); ylabel('PSD [$V^2/Hz$]');
|
||||||
xlim([1, 500]);
|
xlim([0.1, 500]);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+NAME: fig:intrumental_noise_V
|
#+NAME: fig:intrumental_noise_V
|
||||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||||
#+begin_src matlab :var filepath="figs/intrumental_noise_V.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
|
#+begin_src matlab :var filepath="figs/intrumental_noise_V.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
<<plt-matlab>>
|
<<plt-matlab>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
@ -363,12 +363,12 @@ This is then further converted into velocity and compared with the ground veloci
|
|||||||
hold off;
|
hold off;
|
||||||
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
set(gca, 'xscale', 'log'); set(gca, 'yscale', 'log');
|
||||||
xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
|
xlabel('Frequency [Hz]'); ylabel('PSD [$m/s/\sqrt{Hz}$]');
|
||||||
xlim([1, 500]);
|
xlim([0.1, 500]);
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
#+NAME: fig:intrumental_noise_velocity
|
#+NAME: fig:intrumental_noise_velocity
|
||||||
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
#+HEADER: :tangle no :exports results :results value raw replace :noweb yes
|
||||||
#+begin_src matlab :var filepath="figs/intrumental_noise_velocity.pdf" :var figsize="wide-tall" :post pdf2svg(file=*this*, ext="png")
|
#+begin_src matlab :var filepath="figs/intrumental_noise_velocity.pdf" :var figsize="full-tall" :post pdf2svg(file=*this*, ext="png")
|
||||||
<<plt-matlab>>
|
<<plt-matlab>>
|
||||||
#+end_src
|
#+end_src
|
||||||
|
|
||||||
|